Further research indicates that you can't ALTER a memory optimized table. You can't even add or change indexes. It seems that this table type is pretty limited at this point. Have to wait for a later release of 2014.
In digging a bit further I found the C code and read some more of the whitepapers on Hekaton. They explain why some of the restrictions are there (mostly performance) and when I read those I saw why some others are not included either.
Basically, if you were writing an in-memory DB from scratch, you probably wouldn't include most of those things either.